STACKED SEARCH FOR GRAVITATIONAL WAVES FROM
THE 2006 SGR 1900+14 STORM
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Citation
Abbott, B. P., R. Abbott, R. Adhikari, P. Ajith, B. Allen, G. Allen,
R. S. Amin, et al. “STACKED SEARCH FOR GRAVITATIONAL
WAVES FROM THE 2006 SGR 1900+14 STORM.” The
Astrophysical Journal 701, no. 2 (July 30, 2009): L68–L74. ©
2009 American Astronomical Society.
As Published
http://dx.doi.org/10.1088/0004-637x/701/2/l68
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Institute of Physics/American Astronomical Society
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Final published version
Accessed
Thu May 26 03:07:02 EDT 2016
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http://hdl.handle.net/1721.1/95904
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The Astrophysical Journal, 701:L68–L74, 2009 August 20
C 2009.
doi:10.1088/0004-637X/701/2/L68
The American Astronomical Society. All rights reserved. Printed in the U.S.A.
STACKED SEARCH FOR GRAVITATIONAL WAVES FROM THE 2006 SGR 1900+14 STORM
B. P. Abbott1 , R. Abbott1 , R. Adhikari1 , P. Ajith2 , B. Allen2,3 , G. Allen4 , R. S. Amin5 , S. B. Anderson1 ,
W. G. Anderson3 , M. A. Arain6 , M. Araya1 , H. Armandula1 , P. Armor3 , Y. Aso1 , S. Aston7 , P. Aufmuth8 , C. Aulbert2 ,
S. Babak9 , P. Baker10 , S. Ballmer1 , C. Barker11 , D. Barker11 , B. Barr12 , P. Barriga13 , L. Barsotti14 , M. A. Barton1 ,
I. Bartos15 , R. Bassiri12 , M. Bastarrika12 , B. Behnke9 , M. Benacquista16 , J. Betzwieser1 , P. T. Beyersdorf17 ,
I. A. Bilenko18 , G. Billingsley1 , R. Biswas3 , E. Black1 , J. K. Blackburn1 , L. Blackburn14 , D. Blair13 , B. Bland11 ,
T. P. Bodiya14 , L. Bogue19 , R. Bork1 , V. Boschi1 , S. Bose20 , P. R. Brady3 , V. B. Braginsky18 , J. E. Brau21 , D. O. Bridges19 ,
M. Brinkmann2 , A. F. Brooks1 , D. A. Brown22 , A. Brummit23 , G. Brunet14 , A. Bullington4 , A. Buonanno24 ,
O. Burmeister2 , R. L. Byer4 , L. Cadonati25 , J. B. Camp26 , J. Cannizzo26 , K. C. Cannon1 , J. Cao14 , L. Cardenas1 ,
S. Caride27 , G. Castaldi28 , S. Caudill5 , M. Cavaglià29 , C. Cepeda1 , T. Chalermsongsak1 , E. Chalkley12 , P. Charlton30 ,
S. Chatterji1 , S. Chelkowski7 , Y. Chen9,31 , N. Christensen32 , C. T. Y. Chung33 , D. Clark4 , J. Clark34 , J. H. Clayton3 ,
T. Cokelaer34 , C. N. Colacino35 , R. Conte36 , D. Cook11 , T. R. C. Corbitt14 , N. Cornish10 , D. Coward13 , D. C. Coyne1 ,
J. D. E. Creighton3 , T. D. Creighton16 , A. M. Cruise7 , R. M. Culter7 , A. Cumming12 , L. Cunningham12 , S. L. Danilishin18 ,
K. Danzmann2,8 , B. Daudert1 , G. Davies34 , E. J. Daw37 , D. DeBra4 , J. Degallaix2 , V. Dergachev27 , S. Desai38 ,
R. DeSalvo1 , S. Dhurandhar39 , M. Dı́az16 , A. Dietz34 , F. Donovan14 , K. L. Dooley6 , E. E. Doomes40 , R. W. P. Drever41 ,
J. Dueck2 , I. Duke14 , J.-C. Dumas13 , J. G. Dwyer15 , C. Echols1 , M. Edgar12 , A. Effler11 , P. Ehrens1 , E. Espinoza1 ,
T. Etzel1 , M. Evans14 , T. Evans19 , S. Fairhurst34 , Y. Faltas6 , Y. Fan13 , D. Fazi1 , H. Fehrmann2 , L. S. Finn38 , K. Flasch3 ,
S. Foley14 , C. Forrest42 , N. Fotopoulos3 , A. Franzen8 , M. Frede2 , M. Frei43 , Z. Frei35 , A. Freise7 , R. Frey21 , T. Fricke19 ,
P. Fritschel14 , V. V. Frolov19 , M. Fyffe19 , V. Galdi28 , J. A. Garofoli22 , I. Gholami9 , J. A. Giaime19,5 , S. Giampanis2 ,
K. D. Giardina19 , K. Goda14 , E. Goetz27 , L. M. Goggin3 , G. González5 , M. L. Gorodetsky18 , S. Goßler2 , R. Gouaty5 ,
A. Grant12 , S. Gras13 , C. Gray11 , M. Gray44 , R. J. S. Greenhalgh23 , A. M. Gretarsson45 , F. Grimaldi14 , R. Grosso16 ,
H. Grote2 , S. Grunewald9 , M. Guenther11 , E. K. Gustafson1 , R. Gustafson27 , B. Hage8 , J. M. Hallam7 , D. Hammer3 ,
G. D. Hammond12 , C. Hanna1 , J. Hanson19 , J. Harms46 , G. M. Harry14 , I. W. Harry34 , E. D. Harstad21 , K. Haughian12 ,
K. Hayama16 , J. Heefner1 , I. S. Heng12 , A. Heptonstall1 , M. Hewitson2 , S. Hild7 , E. Hirose22 , D. Hoak19 , K. A. Hodge1 ,
K. Holt19 , D. J. Hosken47 , J. Hough12 , D. Hoyland13 , B. Hughey14 , S. H. Huttner12 , D. R. Ingram11 , T. Isogai32 , M. Ito21 ,
A. Ivanov1 , B. Johnson11 , W. W. Johnson5 , D. I. Jones48 , G. Jones34 , R. Jones12 , L. Ju13 , P. Kalmus1 , V. Kalogera49 ,
S. Kandhasamy46 , J. Kanner24 , D. Kasprzyk7 , E. Katsavounidis14 , K. Kawabe11 , S. Kawamura50 , F. Kawazoe2 ,
W. Kells1 , D. G. Keppel1 , A. Khalaidovski2 , F. Y. Khalili18 , R. Khan15 , E. Khazanov51 , P. King1 , J. S. Kissel5 ,
S. Klimenko6 , K. Kokeyama50 , V. Kondrashov1 , R. Kopparapu38 , S. Koranda3 , D. Kozak1 , B. Krishnan9 , R. Kumar12 ,
P. Kwee8 , P. K. Lam44 , M. Landry11 , B. Lantz4 , A. Lazzarini1 , H. Lei16 , M. Lei1 , N. Leindecker4 , I. Leonor21 , C. Li31 ,
H. Lin6 , P. E. Lindquist1 , T. B. Littenberg10 , N. A. Lockerbie52 , D. Lodhia7 , M. Longo28 , M. Lormand19 , P. Lu4 ,
M. Lubinski11 , A. Lucianetti6 , H. Lück2,8 , B. Machenschalk9 , M. MacInnis14 , M. Mageswaran1 , K. Mailand1 ,
I. Mandel49 , V. Mandic46 , S. Márka15 , Z. Márka15 , A. Markosyan4 , J. Markowitz14 , E. Maros1 , I. W. Martin12 ,
R. M. Martin6 , J. N. Marx1 , K. Mason14 , F. Matichard5 , L. Matone15 , R. A. Matzner43 , N. Mavalvala14 , R. McCarthy11 ,
D. E. McClelland44 , S. C. McGuire40 , M. McHugh53 , G. McIntyre1 , D. J. A. McKechan34 , K. McKenzie44 , M. Mehmet2 ,
A. Melatos33 , A. C. Melissinos42 , D. F. Menéndez38 , G. Mendell11 , R. A. Mercer3 , S. Meshkov1 , C. Messenger2 ,
M. S. Meyer19 , J. Miller12 , J. Minelli38 , Y. Mino31 , V. P. Mitrofanov18 , G. Mitselmakher6 , R. Mittleman14 ,
O. Miyakawa1 , B. Moe3 , S. D. Mohanty16 , S. R. P. Mohapatra25 , G. Moreno11 , T. Morioka50 , K. Mors2 , K. Mossavi2 ,
C. MowLowry44 , G. Mueller6 , H. Müller-Ebhardt2 , D. Muhammad19 , S. Mukherjee16 , H. Mukhopadhyay39 ,
A. Mullavey44 , J. Munch47 , P. G. Murray12 , E. Myers11 , J. Myers11 , T. Nash1 , J. Nelson12 , G. Newton12 , A. Nishizawa50 ,
K. Numata26 , J. O’Dell23 , B. O’Reilly19 , R. O’Shaughnessy38 , E. Ochsner24 , G. H. Ogin1 , D. J. Ottaway47 , R. S. Ottens6 ,
H. Overmier19 , B. J. Owen38 , Y. Pan24 , C. Pankow6 , M. A. Papa9,3 , V. Parameshwaraiah11 , P. Patel1 , M. Pedraza1 ,
S. Penn54 , A. Perreca7 , V. Pierro28 , I. M. Pinto28 , M. Pitkin12 , H. J. Pletsch2 , M. V. Plissi12 , F. Postiglione36 ,
M. Principe28 , R. Prix2 , L. Prokhorov18 , O. Punken2 , V. Quetschke6 , F. J. Raab11 , D. S. Rabeling44 , H. Radkins11 ,
P. Raffai35 , Z. Raics15 , N. Rainer2 , M. Rakhmanov16 , V. Raymond49 , C. M. Reed11 , T. Reed55 , H. Rehbein2 , S. Reid12 ,
D. H. Reitze6 , R. Riesen19 , K. Riles27 , B. Rivera11 , P. Roberts56 , N. A. Robertson1,12 , C. Robinson34 , E. L. Robinson9 ,
S. Roddy19 , C. Röver2 , J. Rollins15 , J. D. Romano16 , J. H. Romie19 , S. Rowan12 , A. Rüdiger2 , P. Russell1 , K. Ryan11 ,
S. Sakata50 , L. Sancho de la Jordana57 , V. Sandberg11 , V. Sannibale1 , L. Santamarı́a9 , S. Saraf58 , P. Sarin14 ,
B. S. Sathyaprakash34 , S. Sato50 , M. Satterthwaite44 , P. R. Saulson22 , R. Savage11 , P. Savov31 , M. Scanlan55 ,
R. Schilling2 , R. Schnabel2 , R. Schofield21 , B. Schulz2 , B. F. Schutz9,34 , P. Schwinberg11 , J. Scott12 , S. M. Scott44 ,
A. C. Searle1 , B. Sears1 , F. Seifert2 , D. Sellers19 , A. S. Sengupta1 , A. Sergeev51 , B. Shapiro14 , P. Shawhan24 ,
D. H. Shoemaker14 , A. Sibley19 , X. Siemens3 , D. Sigg11 , S. Sinha4 , A. M. Sintes57 , B. J. J. Slagmolen44 , J. Slutsky5 ,
J. R. Smith22 , M. R. Smith1 , N. D. Smith14 , K. Somiya31 , B. Sorazu12 , A. Stein14 , L. C. Stein14 , S. Steplewski20 ,
A. Stochino1 , R. Stone16 , K. A. Strain12 , S. Strigin18 , A. Stroeer26 , A. L. Stuver19 , T. Z. Summerscales56 , K.-X. Sun4 ,
M. Sung5 , P. J. Sutton34 , G. P. Szokoly35 , D. Talukder20 , L. Tang16 , D. B. Tanner6 , S. P. Tarabrin18 , J. R. Taylor2 ,
R. Taylor1 , J. Thacker19 , K. A. Thorne19 , K. S. Thorne31 , A. Thüring8 , K. V. Tokmakov12 , C. Torres19 , C. Torrie1 ,
L68
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STACKED SEARCH FOR GRAVITATIONAL WAVES FROM SGR 1900+14
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4
8
31
L69
G. Traylor , M. Trias , D. Ugolini , J. Ulmen , K. Urbanek , H. Vahlbruch , M. Vallisneri , C. van den Broeck34 ,
M. V. van der Sluys49 , A. A. van Veggel12 , S. Vass1 , R. Vaulin3 , A. Vecchio7 , J. Veitch7 , P. Veitch47 , C. Veltkamp2 ,
A. Villar1 , C. Vorvick11 , S. P. Vyachanin18 , S. J. Waldman14 , L. Wallace1 , R. L. Ward1 , A. Weidner2 , M. Weinert2 ,
A. J. Weinstein1 , R. Weiss14 , L. Wen31,13 , S. Wen5 , K. Wette44 , J. T. Whelan9,60 , S. E. Whitcomb1 , B. F. Whiting6 ,
C. Wilkinson11 , P. A. Willems1 , H. R. Williams38 , L. Williams6 , B. Willke2,8 , I. Wilmut23 , L. Winkelmann2 ,
W. Winkler2 , C. C. Wipf14 , A. G. Wiseman3 , G. Woan12 , R. Wooley19 , J. Worden11 , W. Wu6 , I. Yakushin19 ,
H. Yamamoto1 , Z. Yan13 , S. Yoshida61 , M. Zanolin45 , J. Zhang27 , L. Zhang1 , C. Zhao13 , N. Zotov55 , M. E. Zucker14 ,
H. zur Mühlen8 , and J. Zweizig1
(The LIGO Scientific Collaboration62 )
1 LIGO - California Institute of Technology, Pasadena, CA 91125, USA
Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany
3 University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA
4 Stanford University, Stanford, CA 94305, USA
5 Louisiana State University, Baton Rouge, LA 70803, USA
6 University of Florida, Gainesville, FL 32611, USA
7 University of Birmingham, Birmingham B15 2TT, UK
8 Leibniz Universität Hannover, D-30167 Hannover, Germany
9 Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Golm, Germany
10 Montana State University, Bozeman, MT 59717, USA
11 LIGO - Hanford Observatory, Richland, WA 99352, USA
12 University of Glasgow, Glasgow G12 8QQ, UK
13 University of Western Australia, Crawley, WA 6009, Australia
14 LIGO - Massachusetts Institute of Technology, Cambridge, MA 02139, USA
15 Columbia University, New York, NY 10027, USA
16 The University of Texas at Brownsville and Texas Southmost College, Brownsville, TX 78520, USA
17 San Jose State University, San Jose, CA 95192, USA
18 Moscow State University, Moscow 119992, Russia
19 LIGO - Livingston Observatory, Livingston, LA 70754, USA
20 Washington State University, Pullman, WA 99164, USA
21 University of Oregon, Eugene, OR 97403, USA
22 Syracuse University, Syracuse, NY 13244, USA
23 Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, UK
24 University of Maryland, College Park, MD 20742, USA
25 University of Massachusetts, Amherst, MA 01003, USA
26 NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
27 University of Michigan, Ann Arbor, MI 48109, USA
28 University of Sannio at Benevento, I-82100 Benevento, Italy
29 The University of Mississippi, University, MS 38677, USA
30 Charles Sturt University, Wagga Wagga, NSW 2678, Australia
31 Caltech-CaRT, Pasadena, CA 91125, USA
32 Carleton College, Northfield, MN 55057, USA
33 The University of Melbourne, Parkville, VIC 3010, Australia
34 Cardiff University, Cardiff CF24 3AA, UK
35 Eötvös University, ELTE 1053 Budapest, Hungary
36 University of Salerno, 84084 Fisciano (Salerno), Italy
37 The University of Sheffield, Sheffield S10 2TN, UK
38 The Pennsylvania State University, University Park, PA 16802, USA
39 Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
40 Southern University and A&M College, Baton Rouge, LA 70813, USA
41 California Institute of Technology, Pasadena, CA 91125, USA
42 University of Rochester, Rochester, NY 14627, USA
43 The University of Texas at Austin, TX 78712, USA
44 Australian National University, Canberra 0200, Australia
45 Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
46 University of Minnesota, Minneapolis, MN 55455, USA
47 University of Adelaide, Adelaide, SA 5005, Australia
48 University of Southampton, Southampton SO17 1BJ, UK
49 Northwestern University, Evanston, IL 60208, USA
50 National Astronomical Observatory of Japan, Tokyo 181-8588, Japan
51 Institute of Applied Physics, Nizhny Novgorod 603950, Russia
52 University of Strathclyde, Glasgow G1 1XQ, UK
53 Loyola University, New Orleans, LA 70118, USA
54 Hobart and William Smith Colleges, Geneva, NY 14456, USA
55 Louisiana Tech University, Ruston, LA 71272, USA
56 Andrews University, Berrien Springs, MI 49104, USA
57 Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
58 Sonoma State University, Rohnert Park, CA 94928, USA
59 Trinity University, San Antonio, TX 78212, USA
60 Rochester Institute of Technology, Rochester, NY 14623, USA
61 Southeastern Louisiana University, Hammond, LA 70402, USA
Received 2009 May 19; accepted 2009 July 17; published 2009 July 30
2
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ABBOTT ET AL.
Vol. 701
ABSTRACT
We present the results of a LIGO search for short-duration gravitational waves (GWs) associated with the
2006 March 29 SGR 1900+14 storm. A new search method is used, “stacking” the GW data around the times
of individual soft-gamma bursts in the storm to enhance sensitivity for models in which multiple bursts are
accompanied by GW emission. We assume that variation in the time difference between burst electromagnetic
emission and potential burst GW emission is small relative to the GW signal duration, and we time-align GW
excess power time–frequency tilings containing individual burst triggers to their corresponding electromagnetic
emissions. We use two GW emission models in our search: a fluence-weighted model and a flat (unweighted)
model for the most electromagnetically energetic bursts. We find no evidence of GWs associated with either
model. Model-dependent GW strain, isotropic GW emission energy EGW , and γ ≡ EGW /EEM upper limits
are estimated using a variety of assumed waveforms. The stacking method allows us to set the most stringent
model-dependent limits on transient GW strain published to date. We find EGW upper limit estimates (at
a nominal distance of 10 kpc) of between 2 × 1045 erg and 6 × 1050 erg depending on the waveform
type. These limits are an order of magnitude lower than upper limits published previously for this storm
and overlap with the range of electromagnetic energies emitted in soft gamma repeater (SGR) giant flares.
Key words: gamma rays: bursts – gravitational waves – pulsars: individual (SGR 1900+14) – stars: neutron
1. INTRODUCTION
Soft gamma repeaters (SGRs) sporadically emit brief
(∼ 0.1 s) intense bursts of soft gamma-rays. Three of the five
known SGRs have produced rare “giant flare” events with initial
bright, short (∼ 0.2 s) pulses with peak electromagnetic (EM)
luminosities between 1044 and 1047 erg s−1 , placing them among
the most EM luminous events in the universe. According to the
“magnetar” model SGRs are galactic neutron stars with extreme
magnetic fields ∼ 1015 G (Duncan & Thompson 1992). Bursts
may result from the interaction of the star’s magnetic field with
its solid crust, leading to crustal deformations and occasional
catastrophic cracking (Thompson & Duncan 1995; Schwartz
et al. 2005; Horowitz & Kadau 2009) with subsequent excitation of nonradial neutron star f-modes (Andersson & Kokkotas
1998; de Freitas Pacheco 1998; Ioka 2001) and the emission
of GWs (de Freitas Pacheco 1998; Ioka 2001; Horvath 2005;
Owen 2005). For reviews, see Mereghetti (2008) and Woods &
Thompson (2004).
Occasionally, SGRs produce many soft gamma bursts in a
brief period of time; such intense emissions are referred to as
“storms.” We present a search for short-duration GW signals
(0.3 s) associated with multiple bursts in the 2006 March 29
SGR 1900+14 storm (Israel et al. 2008) using data collected
by the Laser Interferometer Gravitational Wave Observatory
(LIGO; Abbott et al. 2009b). The storm light curve, obtained
from the Burst Alert Telescope (BAT) aboard the Swift satellite
(Barthelmy et al. 2005), is shown in Figure 1. It consists of
more than 40 bursts in ∼30 s, including common SGR bursts
and some intermediate flares with durations > 0.5 s. The total
fluence for the storm event was estimated by the Konus-Wind
team to be (1–2) × 10−4 erg cm−2 in the (20–200) keV range
(Golenetskii et al. 2006), implying an isotropic EM energy
EEM = (1–2) × 1042 erg at a nominal distance to SGR 1900+14
of 10 kpc (source location and distance is discussed in Kaplan
et al. 2002). At the time of the storm both of the 4 km LIGO
detectors (located at Hanford, WA and Livingston, LA) were
taking science quality data.
We attempt to improve sensitivity to multiple weak GW burst
signals associated with the storm’s multiple EM bursts by adding
62
http://www.ligo.org
together GW signal power over multiple bursts. In doing so we
assume particular GW emission models, which we describe in
the next section. Figure 2 illustrates the stacking procedure using
the four most energetic bursts in the storm.
2. METHODS
The analysis is performed by the Stack-a-flare pipeline
(Kalmus et al. 2009), which extends the method used in a
recent LIGO search for transient GW associated with individual
SGR bursts (Abbott et al. 2008a) and relies on an excess
power detection statistic (Anderson et al. 2001). To “stack”
N bursts in the storm, we first generate N excess power time–
frequency tilings. These are two-dimensional matrices in time
and frequency produced by combining the two detectors’ data
streams so as to provide sensitivity to correlated signals, as
described in Kalmus et al. (2007). Each tiling element gives
an excess power estimate in the GW detector data stream in a
small period of time δt and a small range of frequency δf . The
time range of each tiling is chosen to be centered on the time of
one of the target EM bursts in the storm. We then align these N
tilings along the time dimension so that times of the target EM
bursts coincide, and perform a weighted addition.
Stacking significantly improves sensitivity to GW emission
under a given model. However, improving detection probability
depends upon stacking according to GW emission models that
correctly describe nature. The storm light curve motivated
two stacking models: a flat-weighted model with an energy
cutoff, which includes the 11 most energetic EM bursts with
unity weighting factors; and an EM-fluence-weighted model
comprised of the 18 most energetic EM bursts. In the flat model,
we assume that a fixed amount of GW energy is released in each
burst independently of its EM energy, provided the EM energy is
above a threshold. The threshold choice is motivated by a clear
separation in EM fluence of the 11 most energetic bursts from
out of the total of ∼40 bursts in the storm observed by BAT.
A histogram of EM fluence of bursts (in terms of BAT counts)
illustrating this separation is shown in Kalmus et al. (2009). In
the EM-fluence-weighted model, we make the hypothesis that
γ ≡ EGW /EEM is constant from burst to burst, i.e., EGW is
always proportional to EEM . Including the 18 most energetic
bursts accounts for 95% of the total EM fluence of the more
No. 2, 2009
STACKED SEARCH FOR GRAVITATIONAL WAVES FROM SGR 1900+14
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Counts/ms [15−100 keV]
800
700
600
500
400
300
200
100
0
0
5
10
15
relative time [s]
20
25
30
Counts/ms [15−100 keV]
800
700
600
500
400
300
200
100
0
0.5
1
1.5
2
relative time [s]
2.5
3
3.5
4
Figure 1. SGR 1900+14 storm light curve with 1 ms bins as seen by the Swift BAT detector in the (15–100) keV band (Barthelmy et al. 2005). Bottom plot shows a
detail. Burst start times are estimated by fitting the steeply rising burst edges; EM fluences are estimated by integrating light curve area under each burst. A 30 bin
running average is shown in addition to the raw light curve. Solid lines are linear fits to rising edges; the boundaries of rising edges were found by examining the first
derivatives in the neighborhoods of the peak locations. Crosses mark burst peaks and intersections of the rising edge fits extrapolated to a linear fit of the noise floor
measured in a quiescent period of data in the 50 s BAT sequence before the start of the storm. The one-sigma timing uncertainty averaged over all measurements is
2.9 ms. X-axis times are relative to 2006 March 29 02:53:09.9 UT at the Swift satellite.
Figure 2. Individual EM bursts inform the stacking of GW data. This figure suggests the stacking procedure and explicitly shows search timescales. The top four plots
are EM light curve time series around individual bursts beginning at 2.0 s, 16.6 s, 18.3 s, and 22.3 s in Figure 1. Simulated GW ringdowns in the fluence-weighted
model are superposed. The bottom plot shows the EM time series simultaneously, and the sum of the hypothetical GW signals. The on-source region of ±2 s is shaded.
In the search, GW data corresponding to the EM time series are transformed to time–frequency power tilings before being added together and therefore there is no
dependence on phase-coherence of GW signals in the analysis; this transformation is not illustrated.
than 40 bursts in the light curve. Both burst samples include the
seven intermediate flares identified in Israel et al. (2008). In the
fluence-weighted model, time–frequency excess power tilings
are weighted according to burst-integrated BAT counts before
stacking. Further details are in Kalmus et al. (2009).
To obtain estimates of the times of EM bursts in the storm,
we measure the intersections of the rapid rising edges of each
burst with the light curve noise floor measured in a quiescent
period of data in the 50 s BAT sequence before the start of
the storm (Figure 1). We correct these times for satellite-togeocenter times-of-flight using the known SGR 1900+14 sky
position and Swift ephemeris, which vary from (17.12 to 17.48)
ms over the ∼30 s duration of the storm. The stack-a-flare
analysis method is robust to relative timing errors smaller than
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ABBOTT ET AL.
GW signal durations (Kalmus et al. 2009). EM fluences are
estimated by integrating detector counts under each burst in
the light curve. We conservatively converted counts to fluences
using the lower bound of the Konus-Wind total fluence range
given above, making the assumption that burst spectra are
constant from burst to burst.
We divide the GW data into an on-source time region, in
which GWs associated with the storm could be expected, and
a background region, with statistically similar noise in which
we do not expect a GW. This is done after data quality cuts
(categories 1 and 2 described in Abbott et al. 2009a) are
applied to the GW data, so as to remove, e.g., periods of
instrumental or data acquisition problems, or nonstationary
noise due to bad weather or other environmental conditions.
The on-source region consists of 4 s of stacked data. Each 4
s region comprising the stack is centered on the time of one
of the EM bursts included in the GW emission stacking model.
Background regions consist of 1000 s of data on either side of the
storm. On-source and background segments are analyzed and
stacked identically, and the stacked time–frequency tilings are
passed through a two-dimensional clustering algorithm resulting
in lists of “analysis events.” Each analysis event corresponds
to one discrete cluster found by the algorithm and consists
of information on the cluster central frequency, central time,
bandwidth, and duration (Kalmus et al. 2009). Background
analysis events due to fluctuating detector noise are used to
estimate the significance of on-source events; significant events,
if any, are subject to vetoes (Abbott et al. 2009a).
Using ±2 s regions around bursts in the storm accounts for
uncertainties in the EM burst times and a possible systematic
delay between GW and EM emission. Although GW emission
in SGRs is expected to occur almost simultaneously with the
EM burst (Ioka 2001), a common bias in trigger times shared
by all bursts in the stacking set of 1 s can be handled with a
±2 s on-source region.
As in Abbott et al. (2008a), this search targets neutron star
fundamental mode ringdowns (RDs) predicted in Andersson
& Kokkotas (1998), de Freitas Pacheco (1998), Ioka (2001),
and Andersson (2003) as well as short-duration GW signals
of unknown waveform. RDs are targeted because f-modes are
the most efficient GW emitters (Andersson & Kokkotas 1998).
We assume that given a neutron star, f-mode frequencies and
damping timescales would be similar from event to event,
and that unknown signals would at least have similar central
frequencies and durations from event to event.
As in Abbott et al. (2008a), we thus focus on two distinct
regions in the target signal time–frequency parameter space.
The first region targets ∼100–400 ms duration signals in the
(1–3) kHz band, which includes f-mode RD signals predicted
in Benhar et al. (2004) for ten realistic neutron star equations of
state. We choose a search band of (1–3) kHz for RD searches,
with a 250 ms time window which was found to give optimal
search sensitivity (Kalmus 2008). The second region targets
∼(5–200) ms duration signals in the (100–1000) Hz band. The
target durations are set by prompt SGR burst timescales (5–
200 ms) and the target frequencies are set by the detector’s
sensitive region. We search in two bands: (100–200) Hz (probing
the region in which the detectors are most sensitive) and
(100–1000) Hz (for full spectral coverage below the RD search
band) using a 125 ms time window. In all, we search in three
frequency bands and two GW emission models (flat and fluenceweighted). This amounts to a total of six 4 s long stacked onsource regions.
Vol. 701
We estimate loudest-event upper limits (Brady et al. 2004)
on GW root-sum-squared strain hrss incident at the detector. We
can construct simulations of impinging GW with a given hrss .
Following Abbott et al. (2005b)
h2rss = h2rss+ + h2rss× ,
where, e.g.,
h2rss+ =
∞
−∞
|h+ |2 dt
(1)
(2)
and h+,× (t) are the two GW polarizations. The relationship
between the GW polarizations and the detector response h(t)
to an impinging GW from a polar angle and azimuth (θ, φ) and
with polarization angle ψ is
h(t) = F+ (θ, φ, ψ)h+ (t) + F× (θ, φ, ψ)h× (t),
(3)
where F+ (θ, φ, ψ) and F× (θ, φ, ψ) are the antenna functions
for the source at (θ, φ) (Thorne 1987). At the time of the storm,
the polarization-independent rms antenna response (F+2 +F×2 )1/2 ,
which indicates the average sensitivity to a given sky location,
was 0.39 for LIGO Hanford observatory and 0.46 for the LIGO
Livingston observatory.
We can also set upper limits on the emitted isotropic GW
emission energy EGW at a source distance R associated with
h+ (t) and h× (t) via (Shapiro & Teukolsky 1983)
EGW
c3
= 4π R
16π G
2
∞
−∞
((ḣ+ )2 + (ḣ× )2 )dt.
(4)
The procedure for estimating loudest-event upper limits in
the individual burst search is detailed in Kalmus (2008), Abbott
et al. (2008a), and Acernese et al. (2008). In brief, the upper limit
is computed in a frequentist framework by injecting artificial
signals into the background data and recovering them with the
search pipeline (see for example Abbott et al. 2005a, 2008b). An
analysis event is associated with each injection, and compared to
the loudest on-source analysis event. The GW strain or isotropic
energy at 90% detection efficiency is the strain or isotropic
energy at which 90% of injections have associated events louder
than the loudest on-source event.
We use the 12 waveform types described in Abbott et al.
(2008a) to establish detector sensitivity and thereby set upper
limits: linearly and circularly polarized RDs with τ = 200 ms
and frequencies in the range (1–3) kHz; and band- and timelimited white noise bursts (WNBs) with durations of 11 ms and
100 ms and frequency bands matched to the two lower frequency
search bands.
These waveforms are used to construct compound injections
determined by the emission model. In the flat model, 11 GW
bursts comprise a compound injection, each is identical, and
our stated hrss and EGW are for one such GW burst in the
compound injection. In the fluence-weighted model, 18 GW
bursts comprise a compound injection, they are weighted (in
amplitude) with the square root of integrated counts, and our
stated hrss and EGW are for the loudest GW burst in the
compound injection. A single polarization angle is chosen
randomly for every compound injection. In assuming that the
bursts emitted are identical up to an amplitude scale factor, we
implicitly assume that the star’s GW emission mechanism and
symmetry axis are constant over bursts in the storm.
No. 2, 2009
STACKED SEARCH FOR GRAVITATIONAL WAVES FROM SGR 1900+14
L73
Table 1
Stack-A-Flare SGR 1900+14 Storm Upper Limits
Simulation Type
N=11 Flat
− 12
−22 Hz
h90%
rss [10
WNB 11ms 100–200 Hz
WNB 100ms 100–200 Hz
WNB 11ms 100–1000 Hz
WNB 100ms 100–1000 Hz
1.3
1.5
3.5
3.8
+0.0+0.17+0.0
RDC 200ms 1090 Hz
RDC 200ms 1590 Hz
RDC 200ms 2090 Hz
RDC 200ms 2590 Hz
4.5
6.4
9.3
11
+0.045+0.59+0.0
9.3
14
20
25
+0.0+1.2+0.95
RDL 200ms 1090 Hz
RDL 200ms 1590 Hz
RDL 200ms 2090 Hz
RDL 200ms 2590 Hz
+0.0+0.19+0.0
+0.0+0.45+0.0
+0.0+0.50+0.0
+0.19+0.84+0.0
+0.28+1.8+0.41
+0.34+2.2+0.32
+0.42+1.8+1.1
+1.2+3.9+1.4
+1.8+5.0+3.0
N=18 Fluence-Weighted
90%
EGW
[erg]
γUL
= 1.5
= 1.7
= 3.9
= 4.3
1.9 × 1045
3 × 104
= 5.2
= 7.4
= 11
= 14
= 11
= 17
= 25
= 33
]
1
−22 Hz− 2 ]
h90%
rss [10
4 × 104
3 × 106
3 × 106
2.1
2.3
5.2
5.6
+0.0+0.27+0.094
1.2 × 1048
5.1 × 1048
2.1 × 1049
4.6 × 1049
2 × 107
8 × 107
3 × 108
8 × 108
7.2
11
14
17
+0.072+0.93+0.33
5.3 × 1048
9 × 107
16
19
27
39
2.4 × 1045
1.8 × 1047
2.0 × 1047
2.6 × 1049
1.0 × 1050
2.6 × 1050
4 × 108
2 × 109
4 × 109
+0.0+0.30+0.098
+0.0+0.67+0.29
+0.0+0.73+0.29
+0.33+1.4+0.44
+0.43+2.8+0.72
+0.50+3.3+1.0
+0.0+2.1+1.6
+0.58+2.5+1.9
+1.6+5.3+2.8
+2.7+7.7+2.5
90%
EGW
[erg]
γUL
= 2.4
= 2.6
= 5.9
= 6.3
5.0 × 1045
6.0 × 1045
4.1 × 1047
4.5 × 1047
3 × 104
3 × 104
2 × 106
2 × 106
= 8.2
= 13
= 18
= 21
3.0 × 1048
1.5 × 1049
4.9 × 1049
1.0 × 1050
2 × 107
8 × 107
3 × 108
5 × 108
= 18
= 23
= 34
= 50
1.5 × 1049
5.1 × 1049
1.9 × 1050
6.2 × 1050
8 × 107
3 × 108
1 × 109
3 × 109
Notes. Superscripts account for statistical and systematic errors as described in Section 3. Upper limit estimates on γ ≡ EGW /EEM are computed assuming
that spectra are constant from burst to burst, and using a BAT counts-to-fluence conversion factor estimated using the lower bound of the total fluence measured
by Konus-Wind during the storm.
51
10
50
10
49
E90%
[erg]
GW
10
48
10
47
10
fluence−weighted
46
N=11 flat model
10
45
10
0
500
1000
1500
2000
frequency [Hz]
2500
3000
Figure 3. Stack-a-flare SGR 1900+14 storm isotropic energy upper limit
estimates at 10 kpc, for flat and fluence-weighted emission models. We set
upper limits at characteristic points in the signal parameter space in order to
quantify the meaning of our nondetection result. Uncertainties have been folded
in. Vertical lines indicate boundaries of the three distinct search frequency bands.
Crosses and circles indicate linearly and circularly polarized RDs, respectively.
Triangles and squares represent 11 ms and 100 ms band- and time-limited
WNBs, respectively. Symbols are placed at the waveform central frequency.
These results reflect the noise curves of the detectors.
3. RESULTS
We find no statistically significant GW signal associated with
the SGR 1900+14 storm. The significance of on-source analysis
events is inferred by noting the rate at which background
analysis events of equal or greater loudness occur. We examined
4 s stacked on-source regions in the flat and fluence-weighted
models in the three search bands. The most significant on-source
analysis event from these six searches was from the flat model in
the (100–1000) Hz band and had a corresponding background
rate of 5.0 × 10−2 Hz (1 per 20 s) in that search.
Table 1 and Figure 3 give model-dependent loudest-event
upper limits at 90% detection efficiency computed for the GW
signal associated with the single loudest EM burst. We give
strain upper limits (h90%
rss ) and isotropic emission energy upper
90%
).
limits at a nominal SGR 1900+14 distance of 10 kpc (EGW
90%
/EEM , a source-distanceWe also give upper limits γUL = EGW
independent measure of the extent to which an energy upper
limit probes the GW emission efficiency, calculated using a
conservative estimate of 1.0 × 10−4 erg cm−2 for the total
fluence of the storm to estimate fluences for individual peaks. In
the fluence-weighted model, γ is the same for each individual
burst. In the flat model, we report the mean value of γ for the
11 bursts.
Superscripts in Table 1 give a systematic error and uncertainties at 90% confidence. (Similar estimates were made for
90%
the EGW
but are not shown in the table.) The first and second
superscripts account for the systematic error and statistical uncertainty, respectively, in the detector calibrations. The third is
the statistical uncertainty from using a finite number of trials
(200) in the Monte Carlos, estimated with the bootstrap method
using 200 ensembles (Efron 1979). The systematic error and the
quadrature sum of the statistical uncertainties are added to the
final sensitivity estimates. One-sigma burst timing uncertainties
from fits of burst rising edges are accounted for in the Monte
Carlo simulations. Estimating uncertainties is further described
in Kalmus et al. (2009).
4. DISCUSSION
The stacked search described here extends the recent LIGO
search for GW associated with the 2004 SGR 1806–20 giant
flare and 190 lesser events from SGR 1806–20 and SGR
1900+14 (Abbott et al. 2008a). That search was the first search
sensitive to neutron star f-modes, and it set individual burst
90%
upper limits EGW
ranging from 3 × 1045 erg to 9 × 1052 erg
(depending on the waveform type and detector antenna factors
and noise characteristics at the time of the burst), but did not
detect any GWs. The best values of γUL in Abbott et al. (2008a),
for the giant flare, were in the range 5 × 101 –6 × 106 depending
on the waveform type.
The upper limits obtained here are a factor of 12 more sensitive in energy than the SGR 1900+14 storm upper limits in
Abbott et al. (2008a), which analyzed the storm in a single
±20 s on-source region. Those previous limits already overlapped the range of EM energies seen in the loudest flares as
well as the range of GW energies predicted by the most extreme
models (Ioka 2001). The flat model gives isotropic energy upper
L74
ABBOTT ET AL.
limits on average a factor of 4 lower than a reference N = 1
(nonstacked) scenario (with a ±2 s on-source region) and a factor of 2 lower than the fluence-weighted model. However, our
storm γ upper limits are still a few hundred times the SGR
1806–20 giant flare γ upper limits, due to the tremendous EM
energy released by the giant flare. There is very little discussion
of γ in the theory literature with which to compare.
The Advanced LIGO detectors promise an improvement in
energy sensitivity of more than a factor of 100. Furthermore,
on 2008 August 22, SGR 0501+4516 was discovered (Holland
et al. 2008; Barthelmy et al. 2008; Palmer & Barthelmy 2008)
and may be located only 1.5 kpc away (Gaensler & Chatterjee
2008; Leahy & Aschenbach 1995). SGR 0501+4516 searches
will thus gain an additional 2 orders of magnitude in energy and
γ upper limits compared to SGRs at 10 kpc. A stacking analysis
of SGR 0501+4516 bursts with Advanced LIGO (a gain of 4
orders of magnitude in energy sensitivity) could therefore reach
γ values below unity, even without another giant flare.
In the future, we plan to carry out stacking searches on both
SGR storms, and also on isolated SGR bursts, as the sensitivity
of detectors in the global network of GW interferometers
continues to improve. For example, enhanced LIGO detectors
will come online this year (2009), and data from the Virgo and
GEO detectors in Europe can be used in future searches as
well. Our stacked upper limits depend on theoretical guidance
as to what weightings and time delays are possible, and the
significance of our results depends on predictions of the range
of EGW and γ ; yet all of these things are scarce. We hope that
our continued efforts to search for GW associated with SGR
and anomalous X-ray pulsar bursts encourage further modeling
of GW emission from these intriguing objects.
The authors are grateful to the Swift team for the SGR
1900+14 storm data. The authors gratefully acknowledge the
support of the United States National Science Foundation
for the construction and operation of the LIGO Laboratory
and the Science and Technology Facilities Council of the
United Kingdom, the Max-Planck-Society, and the State of
Niedersachsen/Germany for support of the construction and
operation of the GEO600 detector. The authors also gratefully
acknowledge the support of the research by these agencies and
by the Australian Research Council, the Council of Scientific
and Industrial Research of India, the Istituto Nazionale di
Fisica Nucleare of Italy, the Spanish Ministerio de Educación
y Ciencia, the Conselleria d’Economia Hisenda i Innovació
Vol. 701
of the Govern de les Illes Balears, the Royal Society, the
Scottish Funding Council, the Scottish Universities Physics
Alliance, The National Aeronautics and Space Administration,
the Carnegie Trust, the Leverhulme Trust, the David and Lucile
Packard Foundation, the Research Corporation, and the Alfred
P. Sloan Foundation. This Letter is LIGO-P0900024.
REFERENCES
Abbott, B. P., et al. 2005a, Phys. Rev. D, 72, 082001
Abbott, B. P., et al. 2005b, Phys. Rev. D, 72, 062001
Abbott, B. P., et al. 2008a, Phys. Rev. Lett., 101, 211102
Abbott, B. P., et al. 2008b, Phys. Rev. D, 77, 062004
Abbott, B. P., et al. 2009a, arXiv:0905.0020
Abbott, B. P., et al. 2009b, Reports on Progress in Physics, 72, 076901
Acernese, F. 2008, Class. Quant. Grav., 25, 5001A
Anderson, W. G., Brady, P. R., Creighton, J. D., & Flanagan, É. É. 2001, Phys.
Rev. D, 63, 042003
Andersson, N. 2003, Class. Quant. Grav., 20, 105
Andersson, N., & Kokkotas, K. D. 1998, MNRAS, 299, 1059
Barthelmy, S., et al. 2005, Space Sci. Rev., 120, 143
Barthelmy, S., et al. 2008, GCN Circ. 8113
Benhar, O., Ferrari, V., & Gualtieri, L. 2004, Phys. Rev. D, 70, 124015
Brady, P. R., Creighton, J. D. E., & Wiseman, A. G. 2004, Class. Quant. Grav.,
21, S1775
de Freitas Pacheco, J. A. 1998, A&A, 336, 397
Duncan, R. C., & Thompson, C. 1992, ApJ, 392, L9
Efron, B. 1979, Ann. Stat., 7, 1
Gaensler, B. M., & Chatterjee, S. 2008, GCN Circ. 8149
Golenetskii, S., et al. 2006, GCN Circ. 4946
Holland, S. T., et al. 2008, GCN Circ. 8112
Horowitz, C. J., & Kadau, K. 2009, Phys. Rev. Lett., 102, 191102
Horvath, J. E. 2005, Mod. Phys. Lett. A, 20, 2799
Ioka, K. 2001, MNRAS, 327, 639
Israel, G. L., et al. 2008, ApJ, 685, 1114
Kalmus, P. 2008, PhD thesis, Columbia University
Kalmus, P., Cannon, K. C., Márka, S., & Owen, B. J. 2009, arXiv:0904.4906
Kalmus, P., Khan, R., Matone, L., & Márka, S. 2007, Class. Quant. Grav., 24,
S659
Kaplan, D. L., Kulkarni, S. R., Frail, D. A., & van Kerkwijk, M. H. 2002, ApJ,
566, 378
Leahy, D. A., & Aschenbach, B. 1995, A&A, 293, 853
Mereghetti, S. 2008, A&AR, 15, 225
Owen, B. J. 2005, Phys. Rev. Lett., 95, 211101
Palmer, D., & Barthelmy, S. 2008, GCN Circ. 8115
Schwartz, S. J., et al. 2005, ApJ, 627, L129
Shapiro, S., & Teukolsky, S. 1983, Black Holes, White Dwarfs, and Neutron
Stars (New York: Wiley)
Thompson, C., & Duncan, R. C. 1995, MNRAS, 275, 255
Thorne, K. S. 1987, in 300 Years of Gravitation, ed. W. Hawking & S. W. Israel
(Cambridge: Cambridge Univ. Press), 417
Woods, P. M., & Thompson, C. 2004, in Compact Stellar X-Ray Sources, ed.
W. G. H. Lewin & M. van der Klis (Cambridge: Cambridge Univ. Press)